1. Field of the Invention
The present invention relates to an interferometer apparatus which can correct a measurement error caused by a fluctuation or turbulence of air caused by an environmental change, i.e., a change in refractive index of air.
2. Related Background Art
Conventionally, a measurement error, which is caused by a change in refractive index of air due to an environmental change, and is included in a measurement value associated with the displacement amount or position of an object to be measured obtained from an interferometer apparatus, is corrected by measuring the temperature, pressure, humidity, and the like of air near a measurement beam which travels to and from the object to be measured using environment measurement sensors, and by executing a predetermined calculation based on the measured values from the environment measurement sensors and the measured value of the object to be measured by the measurement beam.
Also, as a conventional interferometer apparatus which corrects a change in refractive index of air as one of environmental changes, for example, Japanese Laid-Open Patent Application No. 60-263801 is known. In an apparatus disclosed in Japanese Laid-Open Patent Application No. 60-263801, as shown in FIG. 1, a laser beam emitted from a laser source 31 is split into two beams by a beam splitter 32. One beam L.sub.2 transmitted through the beam splitter 32 is reflected, as a measurement beam, by a measurement-side reflection member 34 which is arranged to be movable in the right-and-left direction in FIG. 1, and propagates toward the beam splitter 32 again. On the other hand, the other beam L.sub.3 reflected by the beam splitter 32 is reflected, as a reference beam, by a reference-side reflection member 35, fixed to a base, via a reflection mirror 33, and propagates toward the beam splitter 32 again via the reflection mirror 33. The beam splitter 32 combines the measurement beam L2 and the reference beam L.sub.3 to be a beam L.sub.4, and the beam L.sub.4 is received by a photo-electric detector 36. Thus, the moving amount of the reflection member 34 as an object to be measured can be detected.
In this apparatus, the influence caused by a fluctuation of air is corrected by arranging the measurement- and reference-side reflection members 33 and 34 at almost equal positions, so that the reference- and measurement-optical path lengths in a portion influenced by the fluctuation of air become equal to each other.
However, in the conventional apparatus shown in FIG. 1, when the reflection member 34 as the object to be measured largely moves, the optical path difference between the measurement and reference beams L.sub.2 and L.sub.3 increases. As a result, since a measurement error becomes too large to be ignored, the influence of a change in refractive index of air caused by, e.g., a fluctuation of air cannot be fundamentally eliminated.
U.S. Pat. No. 4,984,891 proposes an interferometer apparatus which is not influenced by a change in refractive index of air, as shown in FIGS. 2A to 2C. FIG. 2A is a side view showing the arrangement of an interferometer apparatus, FIG. 2B is a plan view when FIG. 2A is viewed from the top, and FIG. 2C is a side view when FIG. 2A is viewed from the left side of the plane of the drawing.
This apparatus will be described below with reference to FIGS. 2A to 2C. A movable mirror 106 is fixed to one end of a stage ST which mounts, e.g., a wafer W as an object to be measured. The movable mirror 106 has first and second reflection surfaces 106a and 106b, which are arranged to be separated by a predetermined distance l.sub.2 along the measurement direction.
A laser beam emitted from a laser source 101 is incident on a beam-splitting prism 102 in which a semi-transparent surface BS is formed on a joint surface between two prisms (102a and 102b), and is split by the beam-splitting surface BS into two beams in the vertical direction.
A laser beam reflected by the beam-splitting surface BS is incident on an upper portion of a polarization prism 103 via a reflection surface R formed on one surface of the semi-transparent prism 102, and a laser beam transmitted through the beam-splitting surface BS is incident on a lower portion of the polarization prism 103. The polarization prism 103 is constituted by joining two rectangular prisms, and a polarization splitting surface PBS is formed on the joint surface.
The laser beams incident on the upper and lower portions of the polarization prism 103 are polarized and split by the polarization splitting surface PBS in the polarization prism 103 into reference and measurement beams. More specifically, the polarization splitting surface PBS allows p-polarized light components, which oscillate in a direction parallel to the plane of the drawing of FIG. 2B, to pass therethrough as a reference beam, and reflects s-polarized light components, which oscillate in a direction perpendicular to the plane of the drawing of FIG. 2B, as a measurement beam.
The reference beams transmitted through the polarization splitting surface PBS pass through a quarterwave plate 104a joined to the exit surface (one surface of a rectangular prism 103b) of the polarization prism 103, are reflected by a reference reflection mirror 105 arranged at the end face of the quarterwave plate 104a, pass through the quarterwave plate 104a again, and propagate toward the polarization splitting surface PBS. At this time, since the reference beams reciprocally pass through the quarterwave plate 104a, the plane of polarization is rotated through 90.degree., and these beams are converted into s-polarized light beams. Therefore, the reference beams are reflected by the polarization splitting surface PBS, and propagate toward a polarization plate 107 joined to the exit side of the polarization prism 103.
On the other hand, the measurement beams reflected by the polarization splitting surface PBS pass through a quarterwave plate 104b joined to the exit-side surface (one surface of a rectangular prism 103a) of the polarization prism 103, and propagate toward the reflection mirror 106 fixed to one end of the stage ST. As shown in FIG. 2A, a first measurement beam, which is reflected by the upper portion of the polarization splitting surface PBS in the polarization prism 103, and passes through the upper portion of the quarterwave plate 104b, is reflected by the first reflection surface 106a as the upper portion of the reflection mirror 106, passes the quarterwave plate 104b again, and propagates toward the polarization splitting surface PBS. At this time, since the measurement beams reciprocally pass through the quarterwave plate 104b, the plane of polarization thereof is rotated through 90.degree., and the beams are converted into p-polarized light beams. Therefore, the measurement beams are transmitted through the polarization splitting surface PBS, and propagate toward the polarization plate 107 joined to the exit side of the polarization prism 103.
As described above, the measurement and reference beams, which pass through the upper portion of the polarization splitting surface PBS and propagate toward the polarization plate 107, pass through the polarization plate 107 and interfere with each other. Based on the interference light, a first optical path difference measuring device 108a generates an output A associated with the displacement amount of the first reflection surface 106a as the upper portion of the reflection mirror 106. Also, the measurement and reference beams, which pass through the lower portion of the polarization splitting surface PBS and propagate toward the polarization plate 107, pass through the polarization plate 107 and interfere with each other. Based on the interference light, a second optical path difference measuring device 108b generates an output B associated with the displacement amount of the second reflection surface 106b as the lower portion of the reflection mirror 106.
The two outputs from the optical path difference measuring devices (108a and 108b) are input to a calculator 109, and are used in a predetermined calculation. If the output A from the first optical path difference measuring device 108a is represented by X.sub.A, the output B from the second optical path difference measuring device 108b is represented by X.sub.B, the displacement amount of the stage ST is represented by x, the refractive index of air at the origin (at the beginning of measurement or upon resetting) of measurement where the displacement amount is zero is represented by n, a change in refractive index of air caused by, e.g., a fluctuation of air is represented by .DELTA.n, the distance in air between the second reflection surface 106b and the quarterwave plate 104b (or interferometer) is represented by l.sub.1, and the distance in air between the first reflection surface 106a and the second reflection surface 106b is represented by l.sub.2, the two outputs (X.sub.A and X.sub.B) from the optical path difference measuring devices (108a and 108b) are respectively given by formulas (1) below: EQU X.sub.A =xn+(l.sub.1 +l.sub.2 +x).DELTA.n EQU X.sub.B =xn+(l.sub.1 +x).DELTA.n (1)
Also, the calculation formula in the calculator 109 is given by formula (2) below by eliminating .DELTA.n from two formulas (1): ##EQU1##
When the calculation given by formula (2) is executed by the calculator 109, an output result, which is free from the influence of the change in refractive index of air, is generated, and a high-precision position measurement of the stage ST is realized.
However, the prior art shown in FIGS. 2A to 2C suffers a fatal problem that errors of two interferometer apparatuses themselves are amplified in principle. When the distance l.sub.2 between the two reflection surfaces formed on one end on the stage as an object to be measured is decreased, precision capable of compensating for a change in refractive index of air caused by, e.g., a fluctuation of air is decreased.
It is, therefore, an object of the present invention to provide an interferometer apparatus, which can solve the problems of the above-mentioned conventional apparatuses, can precisely correct a measurement error caused by a change in refractive index due to a fluctuation of a gas such as air, and always allows high-precision, stable measurements.